Non-Symmetric Basic Hypergeometric Polynomials and Representation Theory for Confluent Cherednik Algebras

Abstract

In this paper we introduce a basic representation for the confluent Cherednik algebras ${\mathcal{H}}_{\mathrm{V}}$, ${\mathcal{H}}_{\mathrm{III}}$, ${\mathcal{H}}_{\mathrm{III}}^{D_7}$ and ${\mathcal{H}}_{\mathrm{III}}^{D_8}$ defined in arXiv:1307.6140. To prove faithfulness of this basic representation, we introduce the non-symmetric versions of the continuous dual $q$-Hahn, Al-Salam-Chihara, continuous big $q$-Hermite and continuous $q$-Hermite polynomials.

References in corpus (1)

• The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case